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arXiv · 2312.14545

Inverse scattering problem for operators with a finite dimensional non-local potential

Vladimir A. Zolotarev
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Abstract

Scattering problem for a self-adjoint integro-differential operator, which is the sum of the operator of second derivative and of a finite-dimensional self-adjoint operator, is studied. Jost solutions are found and it is shown that the scattering function has a multiplicative structure, besides, each of the multipliers is a scattering coefficient for a pair of self-adjoint operators, one of which is a one-dimensional perturbation of the other. Solution of the inverse problem is based upon the solutions to the inverse problem for every multiplier. A technique for finding parameters of the finite-dimensional perturbation via the scattering data is described.

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Vladimir A. Zolotarev. 2023-12-22. Inverse scattering problem for operators with a finite dimensional non-local potential. https://arxiv.org/abs/2312.14545

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